{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "view-in-github"
   },
   "source": [
    "<a href=\"https://colab.research.google.com/github/jermwatt/machine_learning_refined/blob/main/notes/5_Linear_regression/5_6_Multi.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "8bGRk2zt_eiR"
   },
   "source": [
    "## Chapter 5: Linear regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook contains interactive content from an early draft of the university textbook <a href=\"https://github.com/neonwatty/machine-learning-refined/tree/main\">\n",
    "Machine Learning Refined (2nd edition) </a>.\n",
    "\n",
    "The final draft significantly expands on this content and is available for <a href=\"https://github.com/neonwatty/machine-learning-refined/tree/main/chapter_pdfs\"> download as a PDF here</a>."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "3cM5WBw7_eiT"
   },
   "source": [
    "# 5.6 Multi-Output Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "PCt5rp7n_eiT"
   },
   "source": [
    "Thus far we have assumed that datapoints for linear regression consist of $N$ dimensional *vector valued* inputs and *scalar-valued* outputs.  That is, a prototypical datapoint takes the form  $\\left(\\mathbf{x}_p,\\,y_p\\right)$ where $\\mathbf{x}_p$ is an $N$ dimensional *input vector* and a $y_p$ is a *scalar* output.  While this configuration covers the vast majority of regression cases one may well encounter in practice, it is possible to perform (linear) regression where both *input* and *output* are *vector-valued*.  This is often called *multiple-output regression*, and in this Section we describe how to extend the basic elements of this Chapter to properly handle it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "kRtCzhwG_eiT",
    "outputId": "0e7bc328-cc06-402e-e0b7-6d130ec56ced"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: github-clone in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (1.2.0)\n",
      "Requirement already satisfied: requests>=2.20.0 in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (from github-clone) (2.32.3)\n",
      "Requirement already satisfied: docopt>=0.6.2 in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (from github-clone) (0.6.2)\n",
      "Requirement already satisfied: charset-normalizer<4,>=2 in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (from requests>=2.20.0->github-clone) (3.4.0)\n",
      "Requirement already satisfied: idna<4,>=2.5 in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (from requests>=2.20.0->github-clone) (3.10)\n",
      "Requirement already satisfied: urllib3<3,>=1.21.1 in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (from requests>=2.20.0->github-clone) (2.2.3)\n",
      "Requirement already satisfied: certifi>=2017.4.17 in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (from requests>=2.20.0->github-clone) (2024.12.14)\n",
      "\n",
      "\u001b[1m[\u001b[0m\u001b[34;49mnotice\u001b[0m\u001b[1;39;49m]\u001b[0m\u001b[39;49m A new release of pip is available: \u001b[0m\u001b[31;49m24.2\u001b[0m\u001b[39;49m -> \u001b[0m\u001b[32;49m24.3.1\u001b[0m\n",
      "\u001b[1m[\u001b[0m\u001b[34;49mnotice\u001b[0m\u001b[1;39;49m]\u001b[0m\u001b[39;49m To update, run: \u001b[0m\u001b[32;49mpip install --upgrade pip\u001b[0m\n",
      "chapter_5_datasets already cloned!\n",
      "chapter_5_library already cloned!\n"
     ]
    }
   ],
   "source": [
    "# install github clone - allows for easy cloning of subdirectories\n",
    "!pip install github-clone\n",
    "from pathlib import Path \n",
    "\n",
    "# clone datasets\n",
    "if not Path('chapter_5_datasets').is_dir():\n",
    "    !ghclone https://github.com/neonwatty/machine-learning-refined-notes-assets/tree/main/notes/5_Linear_regression/chapter_5_datasets\n",
    "else:\n",
    "    print('chapter_5_datasets already cloned!')\n",
    "\n",
    "# clone library subdirectory\n",
    "if not Path('chapter_5_library').is_dir():\n",
    "    !ghclone https://github.com/neonwatty/machine-learning-refined-notes-assets/tree/main/notes/5_Linear_regression/chapter_5_library\n",
    "else:\n",
    "    print('chapter_5_library already cloned!')\n",
    "\n",
    "# append path for local library, data, and image import\n",
    "import sys\n",
    "sys.path.append('./chapter_5_library')\n",
    "sys.path.append('./chapter_5_datasets') \n",
    "\n",
    "# import section helper\n",
    "import section_5_6_helpers\n",
    "\n",
    "# dataset paths\n",
    "data_path_1 = 'chapter_5_datasets/linear_2output_regression.csv'\n",
    "\n",
    "# standard imports\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# import autograd-wrapped numpy\n",
    "import autograd.numpy as np\n",
    "\n",
    "# this is needed to compensate for matplotlib notebook's tendancy to blow up images when plotted inline\n",
    "%matplotlib inline\n",
    "from matplotlib import rcParams\n",
    "rcParams['figure.autolayout'] = True\n",
    "\n",
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "7tRTfIsc_eiU"
   },
   "source": [
    "##  Notation and modeling"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "2XpH0wJU_eiU"
   },
   "source": [
    "Suppose now that instead of being *scalar-valued* the output of a regression dataset were *vector-valued*.  That is our datapoints \n",
    "\n",
    "\\begin{equation}\n",
    " \\left(\\mathbf{x}_{1}^{\\,},\\mathbf{y}_{1}^{\\,}\\right),\\,\\left(\\mathbf{x}_{2}^{\\,},\\mathbf{y}_{2}^{\\,}\\right),\\,...,\\,\\left(\\mathbf{x}_{P}^{\\,},\\mathbf{y}_{P}^{\\,}\\right)\n",
    "\\end{equation}\n",
    "\n",
    "have both *vector-valued* input *and* output.  The $p^{th}$ point $\\left(\\mathbf{x}_{p}^{\\,},\\mathbf{y}_{p}^{\\,}\\right)$ has $N$ dimensional input $\\mathbf{x}_p$ and associated $C$ dimensional output $\\mathbf{y}_p$.  While in principle we can treat $\\mathbf{y}_p$ as a $C \\times 1$ column vector, in order to keep the formulae that follows looking similar to what we have already seen in the scalar case we will treat the *input* as a $N\\times 1$ *column* vector and the output as a $1 \\times C$ *row* vector as\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathbf{x}_{p}=\\begin{bmatrix}\n",
    "x_{1,p}\\\\\n",
    "x_{2,p}\\\\\n",
    "\\vdots\\\\\n",
    "x_{N,p}\n",
    "\\end{bmatrix}  \\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,  \\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,  \n",
    "\\mathbf{y}_{p}=\\begin{bmatrix}\n",
    "y_{0,p} &\n",
    "y_{1,p} &\n",
    "\\cdots &\n",
    "y_{C-1,p}\n",
    "\\end{bmatrix}.\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "q8xfQd_Q_eiV"
   },
   "source": [
    "Notice that we index the *output* dimension of $\\mathbf{y}_p$ from $j = 0,1,...,C-1$, starting from $0$ instead of $1$ as with the *input* dimension of $\\mathbf{x}_p$ which ranges from $n = 1,...,N$.  We do this because we will stack a $1$ on top of each input point $\\mathbf{x}_p$ (as shown below) and this entry will have the $0^{th}$ index of our input.\n",
    "\n",
    "Now, notice that to suppose that a *linear* relationship holds between the input $\\mathbf{x}_p$ and *just* the scalar-valued $c^{th}$ dimension of the output $y_{c,p}$ of such a dataset results in precisely the sort of regression framework we have seen thus far.  That is if we denote\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathbf{w}_c=\\begin{bmatrix}\n",
    "w_{0,c}\\\\\n",
    "w_{1,c}\\\\\n",
    "w_{2,c}\\\\\n",
    "\\vdots\\\\\n",
    "w_{N,c}\n",
    "\\end{bmatrix}\n",
    "\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\n",
    "\\mathring{\\mathbf{x}}_p=\\begin{bmatrix}\n",
    "1 \\\\\n",
    "x_{1,p}\\\\\n",
    "x_{2,p}\\\\\n",
    "\\vdots\\\\\n",
    "x_{N,p}\n",
    "\\end{bmatrix},\\,\\,\\,\\, p = 1,...,P\n",
    "\\end{equation}\n",
    "\n",
    "where $\\mathbf{w}_c$ is a set of weights then - if these are tuned properly - the assumption of a linear relationship looks like precisely what we have seen starting in [Section 5.1](https://jermwatt.github.io/machine_learning_refined/notes/5_Linear_regression/5_2_Least.html)\n",
    " \n",
    "\\begin{equation}\n",
    "\\mathring{\\mathbf{x}}_{p}^T  \\overset{\\,}{\\mathbf{w}}_{c}^{\\,}    \\approx \\overset{\\,}{y}_{c,p}^{\\,} \\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,    \\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\, p=1,...,P.\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "vi2gUtGd_eiV"
   },
   "source": [
    "Then let us suppose that a linear relationship holds between the input and all $C$ entries of the output.  If we place each weight vector $\\mathbf{w}_c$ into the $c^{th}$ column of the $\\left(N+1\\right) \\times C$ *weight matrix* $\\mathbf{W}$ as"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ElCvW-7b_eiV"
   },
   "source": [
    "\\begin{equation}\n",
    "\\mathbf{W}=\\begin{bmatrix} \n",
    "w_{0,0}  &  w_{0,1}  &  w_{0,2}  & \\cdots   &  w_{0,C-1}  \\\\\n",
    "w_{1,0}  &  w_{1,1}  &  w_{1,2}  & \\cdots  &   w_{1,C-1}  \\\\\n",
    "w_{2,0}  &  w_{2,1}  &  w_{2,2}  & \\cdots  &  w_{2,C-1}  \\\\\n",
    "\\,\\,\\, {\\vdots}_{\\,\\,\\,}  & {\\vdots}_{\\,\\,\\,}  &  {\\vdots}_{\\,\\,\\,}  &  \\cdots   &    {\\vdots}_{\\,\\,\\,}    \\\\\n",
    "w_{N,0}  &  w_{N,1} & w_{N,2}  &  \\cdots  &  w_{N,C-1}  \\\\\n",
    "\\end{bmatrix}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Wl1EGx5n_eiW"
   },
   "source": [
    "then the entire set of $C$ linear models can be written compactly as $1\\times C$ vector-matrix product\n",
    "\n",
    "\\begin{equation}\n",
    "\\begin{matrix}  \\mathring{\\mathbf{x}}_p^T\\mathbf{W} \\end{matrix}  = \\begin{bmatrix}\n",
    "\\mathring{\\mathbf{x}}_p^T  \\overset{\\,}{\\mathbf{w}}_{0}^{\\,}   &\n",
    "\\mathring{\\mathbf{x}}_p^T  \\overset{\\,}{\\mathbf{w}}_{1}^{\\,}   &\n",
    "\\cdots \\, &\n",
    "\\mathring{\\mathbf{x}}_p^T  \\overset{\\,}{\\mathbf{w}}_{C-1}^{\\,}\n",
    "\\end{bmatrix}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "3J4TL2Cw_eiW"
   },
   "source": [
    "and then the entire set of $C$ linear relationships can likewise be written as \n",
    "\n",
    "\\begin{equation}\n",
    "\\mathring{\\mathbf{x}}_{p}^T  \\overset{\\,}{\\mathbf{W}}_{\\,}^{\\,}    \\approx \\overset{\\,}{\\mathbf{y}}_{p}^{\\,} \\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,    \\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\, p=1,...,P.\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "kZHZYOAB_eiW"
   },
   "source": [
    "But of course this approximation $\\approx$ only truly holds if we can tune the weights $\\mathbf{W}$ properly.  To do this we can invoke any regression cost function - e.g., the Least Squares or Least Absolute Deviations - and properly minimize in order to make this approximation hold as well as possible."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "P9jHgy5K_eiW"
   },
   "source": [
    "## Cost functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "nxDEsn8U_eiX"
   },
   "source": [
    "The thought process involved in deriving a regression cost function for the case of multi-output regression mirrors almost exactly the scalar-output case discussed in Sections [5.2](https://jermwatt.github.io/machine_learning_refined/notes/5_Linear_regression/5_2_Least.html) and [5.3](https://jermwatt.github.io/machine_learning_refined/notes/5_Linear_regression/5_3_Absolute.html).  For example, to derive a Least Squares cost function we begin by taking the difference of both sides in equation (6) above.  However now the error associated with the $p^{th}$ point, written as $\\mathring{\\mathbf{x}}_{p}^T  \\overset{\\,}{\\mathbf{W}}_{\\,}^{\\,}    - \\overset{\\,}{\\mathbf{y}}_{p}^{\\,}$, has $C$ values.  To square this error we must employ the *squared* $\\ell_2$ norm, which is a natural extension of the squaring operation $\\left(\\cdot\\right)^2$ to vectors (described further in Appendix Section).  The Least Squares cost function in this case is then the average of the $\\ell_2$ norm of each point's error as\n",
    "\n",
    "\\begin{equation}\n",
    " g\\left(\\mathbf{W}\\right) = \\frac{1}{P}\\sum_{p=1}^{P} \\left \\Vert \\mathring{\\mathbf{x}}_{p}^T  \\overset{\\,}{\\mathbf{W}}_{\\,}^{\\,}    - \\overset{\\,}{\\mathbf{y}}_{p}^{\\,} \\right \\Vert_2^2 = \\frac{1}{P}\\sum_{p=1}^{P} \\sum_{c=0}^{C-1} \\left( \\mathring{\\mathbf{x}}_{p}^T  \\overset{\\,}{\\mathbf{w}}_{c}^{\\,}   - \\overset{\\,}{y}_{c,p}^{\\,}   \\right)^2\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "yctaKCWU_eiX"
   },
   "source": [
    "When the output takes on scalar value, that is when $C=1$, this reduces to the Least Squares cost we saw in [Section 5.2](https://jermwatt.github.io/machine_learning_refined/notes/5_Linear_regression/5_2_Least.html).\n",
    "\n",
    "Likewise the analagous Least Absolute Deviations (which measures the absolute value of each error as opposed to its square) cost for our present case takes the form\n",
    "\n",
    "\\begin{equation}\n",
    " g\\left(\\mathbf{W}\\right) = \\frac{1}{P}\\sum_{p=1}^{P} \\left \\Vert \\mathring{\\mathbf{x}}_{p}^T  \\overset{\\,}{\\mathbf{W}}_{\\,}^{\\,}    - \\overset{\\,}{\\mathbf{y}}_{p}^{\\,} \\right \\Vert_1 = \\frac{1}{P}\\sum_{p=1}^{P} \\sum_{c=0}^{C-1} \\left\\vert \\mathring{\\mathbf{x}}_{p}^T  \\overset{\\,}{\\mathbf{w}}_{c}^{\\,}   - \\overset{\\,}{y}_{c,p}^{\\,}   \\right\\vert\n",
    "\\end{equation}\n",
    "\n",
    "where $\\left\\Vert \\cdot \\right \\Vert_1$ is the $\\ell_1$ norm, the generalization of the absolute value function for vectors (see the Appendix Section for further information)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "4u4Vy5i1_eiX"
   },
   "source": [
    "These cost functions - like their scalar-valued output analogs described are alwasy convex *regardless of the dataset used*.  \n",
    "\n",
    "They also *decompose over the weights $\\mathbf{w}_c$ associated with each output dimension*.  For example, notice that we can rewrite the right hand side of the Least Absolute Deviations cost above by swpping the summands over $P$ and $C$ giving\n",
    "\n",
    "\\begin{equation}\n",
    " g\\left(\\mathbf{W}\\right) =  \\sum_{c=0}^{C-1} \\left(\\frac{1}{P}\\sum_{p=1}^{P} \\left\\vert \\mathring{\\mathbf{x}}_{p}^T  \\overset{\\,}{\\mathbf{w}}_{c}^{\\,}   - \\overset{\\,}{y}_{c,p}^{\\,}   \\right\\vert\\right)  =  \\sum_{c=0}^{C-1} g_c\\left(\\mathbf{w}_c\\right)\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "kS6MsYI0_eiY"
   },
   "source": [
    "where we have denoted $g_c\\left(\\mathbf{w}_c\\right) = \\frac{1}{P}\\sum_{p=1}^{P} \\left\\vert \\mathring{\\mathbf{x}}_{p}^T  \\overset{\\,}{\\mathbf{w}}_{c}^{\\,}   - \\overset{\\,}{y}_{c,p}^{\\,}   \\right\\vert$.  Since the weights from each of the $C$ problems do not interact we can if desired minimize each $g_c$ for an optimal setting of $\\mathbf{w}_c$ independently, and then take their sum to form the full cost function $g$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "xStFDtPF_eiY"
   },
   "source": [
    "##  Implementing cost functions in `Python`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "iiJ-Z1xs_eiY"
   },
   "source": [
    "Because `Python` has such flexible sytax, we can implement the linear model\n",
    "\n",
    "\\begin{equation}\n",
    "\\text{model}\\left(\\mathbf{x},\\mathbf{W}\\right) =\n",
    "\\mathring{\\mathbf{x}}^T\\mathbf{W}^{\\,} \n",
    "\\end{equation}\n",
    "\n",
    "precisely as we have done before.  In *implementing* this linear combination we need not form the adjusted input $\\mathring{\\mathbf{x}}_{p}$ (by tacking a $1$ on top of the raw input $\\mathbf{x}_p$) and can more easily compute the linear combination by exposing the biases as\n",
    "\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathring{\\mathbf{x}}_{p}^T \\mathbf{W} = \\mathbf{b} + \\mathbf{x}_p^T \\mathbf{\\mathcal{W}}\n",
    "\\end{equation}\n",
    "\n",
    "Here we use the following bias / feature weight notation\n",
    "\n",
    "\n",
    "\\begin{equation}\n",
    "\\text{(biases):}\\,\\, \\mathbf{b} = \\begin{bmatrix} w_{0,0} \\\\ w_{0,1} \\\\ w_{0,2} \\\\ \\vdots \\\\ w_{0,C-1} \\end{bmatrix}\n",
    "\\,\\,\\, \\text{(feature-touching weights):} \\,\\,\\,\\,\\,\\, \\boldsymbol{\\mathcal{W}}\n",
    "=\\begin{bmatrix} \n",
    "w_{0,1}  &  w_{0,2}  & \\cdots   &  w_{0,C-1}  \\\\\n",
    "w_{1,1}  &  w_{1,2}  & \\cdots  &   w_{1,C-1}  \\\\\n",
    "w_{2,1}  &  w_{2,2}  & \\cdots  &  w_{2,C-1}  \\\\\n",
    "\\,\\,\\, {\\vdots}_{\\,\\,\\,}  & {\\vdots}_{\\,\\,\\,}  &  {\\vdots}_{\\,\\,\\,}   &    {\\vdots}_{\\,\\,\\,}    \\\\\n",
    "w_{N,1} & w_{N,2}  &  \\cdots  &  w_{N,C-1}  \\\\\n",
    "\\end{bmatrix}.\n",
    "\\end{equation}\n",
    "\n",
    "This notation is used to match the `Pythonic` slicing operation (as shown in the implementation given below), which we implement in `Python` analagously as\n",
    "\n",
    "                            a = w[0] + np.dot(x_p.T,w[1:])\n",
    "\n",
    "That is $\\mathbf{b} = w[0]$ denotes the bias and $\\mathbf{\\mathcal{W}} = w[1:]$ denotes the remaining feature-touching.  Another reason to implement in this way is that the particular linear combination $\\mathbf{x}_p^T \\mathbf{\\mathcal{W}}_{\\,}^{\\,}$ - implemented using `np.dot` as `np.dot(x_p.T,w[1:])` below - is an especially effecient since `numpy`'s `np.dot` operation is far more effecient than constructing a linear combination in `Python` via an explicit `for` loop."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "id": "YrmKx_Z__eiZ"
   },
   "outputs": [],
   "source": [
    "# compute linear combination of input points\n",
    "def model(x,w):\n",
    "    a = w[0] + np.dot(x.T,w[1:])\n",
    "    return a.T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "wxsqjTSl_eiZ"
   },
   "source": [
    "`Pythonic` implementation of regression cost functions can also be implemented precisely as we have seen previously.  For example, the Least Squares cost can be written as shown below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "id": "awSXGEtI_eiZ"
   },
   "outputs": [],
   "source": [
    "# an implementation of the least squares cost function for linear regression\n",
    "def least_squares(w):    \n",
    "    # compute the least squares cost\n",
    "    cost = np.sum((model(x,w) - y)**2)\n",
    "    return cost/float(np.size(y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "j2N2cKWa_eia"
   },
   "source": [
    "#### <span style=\"color:#a50e3e;\">Example 1: </span> Fitting a linear model to a multi-output regression dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "k_fJ2_qa_eia"
   },
   "source": [
    "In this example we show an example of multi-output linear regression using a toy dataset with input dimension $N=2$ and output dimension $C=2$.  The dataset is shown below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 297
    },
    "id": "y032qJb1_eia",
    "outputId": "d014e7bd-1c4f-43ec-c65c-bdfd20638be2"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# load in data\n",
    "data = np.loadtxt(data_path_1, delimiter=',')\n",
    "x = data[:2,:]\n",
    "y = data[2:,:]\n",
    "\n",
    "# plot\n",
    "view1 = [20,40]; view2 = [20,40]\n",
    "section_5_6_helpers.plot_data(x,y,view1,view2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "vSLZnkox_eib"
   },
   "source": [
    "We use the `Pythonic` Least Squares function shown above, minimizing it using $200$ steps of gradient descent using a steplength / learning rate $\\alpha = 1$.  The cost function history from this run is shown below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 225
    },
    "id": "SrIkYu2K_eib",
    "outputId": "c309307f-528d-4299-fd88-e0d033c738f8"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# setup and run optimization\n",
    "g = least_squares; \n",
    "w = 0.1*np.random.randn(3,2)\n",
    "max_its = 200;\n",
    "alpha_choice = 1;\n",
    "weight_history,cost_history = section_5_6_helpers.gradient_descent(g,alpha_choice,max_its,w)\n",
    "\n",
    "# plot history\n",
    "section_5_6_helpers.static_visualizer().plot_cost_histories([cost_history],start = 0,points = False,labels = ['run 1'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "pgnMvqML_eib"
   },
   "source": [
    "Using the fully trained model from this run of gradient descent we evaluate a fine mesh of points in the region over which the input of this dataset is defined to visualize our linear approximations.  These are shown in light green in the panels below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 297
    },
    "id": "8AIk1dw8_eib",
    "outputId": "d654bbbf-b119-4dd7-a73d-99671e931b4d"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# determine best weights - based on lowest cost value attained\n",
    "ind = np.argmin(cost_history)\n",
    "w_best = weight_history[ind]\n",
    "\n",
    "# form predictor\n",
    "predictor = lambda x: model(x,w_best)\n",
    "\n",
    "# plot data with predictions\n",
    "view1 = [20,40]; view2 = [20,40]\n",
    "section_5_6_helpers.plot_regressions(x,y,predictor,view1,view2)"
   ]
  }
 ],
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